The ACI Code 318M-11 (2011) states that crack width is inherently subject to wide scatter even in ... Bar roughness (bond properties of the reinforcing bars);.
9th International Conference on Short and Medium Span Bridges Calgary, Alberta, Canada, July 15-18, 2014
BEHAVIOUR OF PARTIALLY PRESTRESSED HIGH STRENGTH CONCRETE GIRDERS (CRACKING VIEWPOINT) Shady H. Salem Teaching Assistant, Civil Engineering Department, The British University in Egypt Cairo, Egypt Tarek H. El-Hashimy Teaching Assistant, Structural Engineering Department, Ain Shams University Cairo, Egypt Khalid M. Hilal Assistant Professor, Structural Engineering Department, Ain Shams University Cairo, Egypt Tarek K. Hassan Professor of Concrete Structures, Ain Shams University Cairo, Egypt Ahmed S. Essawy Emeritus Professor of Concrete Structures, Ain Shams University Cairo, Egypt ABSTRACT High strength concrete (HSC) has been widely spread due to the enormous development in the material technology which led to a better quality control, improved mechanical properties and enhanced durability performance of concrete. Partially prestressed concrete is characterized by its cracking behaviour that can be considered as a good alarming system. Through the years, cracking was considered a major influential parameter for durability issues. Recently, researches have encountered a weak correlation between cracking and durability. For this reason, some recent design codes control cracking through the use of proper reinforcement detailing, unlike others who allow cracks to a specific width regarding the users comfort. This research presents an experimental investigation for the cracking behaviour of partially prestressed high strength concrete girders in terms of crack width, spacing and height. Results were compared with different design codes and researchers viewpoints within the service loads. The research aimed to find the most adequate method for calculating these deformations. Thirteen concrete beams were experimented under statically increasing load till failure, while crack pattern had been monitored through different load levels. The studied parameters were the concrete compressive strength, prestressed and non-prestressed steel ratios and the cross section shape.
1. INTRODUCTION High strength concrete (HSC) has been widely spread due to the enormous development in the material technology which led to a better quality control, improved mechanical properties and enhanced durability performance of concrete. Partially prestressed concrete is considered a good alternative solution to reinforced and fully prestressed concrete as it has the advantages of high serviceability control, smaller sections, cost effectiveness and alarming signs of failure via cracking. Karayannis and Chalioris (2012) stated that major design codes on ###-1
concrete structures (ACI318, Eurocode2) have separate detailed sections and provisions for reinforced concrete and fully prestressed concrete elements but they do not include provisions that address directly the partially prestressed concrete elements. Cracking of concrete elements occurs as a result of increasing the stresses below the neutral axis than the concrete tensile strength (modulus of rupture). The concrete cracking can be defined using its pattern which is described by the crack spacing, height and width. Many formulae are currently available to calculate the crack width of partially prestressed concrete beams. The ACI Code 318M-11 (2011) states that crack width is inherently subject to wide scatter even in careful laboratory work and is influenced by shrinkage and other time-dependent effects. Several variables are settled to be the main factors influencing the crack width, these variables are: Stresses in the reinforcement; Concrete cover; Position and arrangement of the reinforcement; Bar roughness (bond properties of the reinforcing bars); Concrete strength; Type and shape of prestressed and non-prestressed reinforcement; Ratio of prestressed to non-prestressed reinforcement; Boundary conditions. Due to high variability of the influencing factors affecting concrete cracking, no universal agreement on a mathematical formulation for the crack width prediction have been introduced through years. This led to another crack control approach independent of crack width calculations, but rather recommends reinforcement spacing that limits the surface cracks to a width that is acceptable in practice, but may vary widely in a given structure. Lately, this approach was adopted by several codes as the ACI318-11(2011). This paper presents an experimental investigation to assess the cracking behaviour of partially prestressed high strength concrete beams. Thirteen concrete beams were experimented under monotonically increasing load till failure, while the crack pattern was monitored through different load levels. The effects of various parameters have been investigated. These parameters were the concrete compressive strength, prestressed and non-prestressed steel ratios and the cross section shape. Results were compared with different design codes and researchers viewpoints within the service loads. The research aimed to find the most adequate method for calculating these deformations. Specimens’ details The experimental program was conducted on thirteen partially prestressed concrete beams with total length of 4800mm. The beams were simply supported with 4500mm clear span and 150mm projection at each end. All beams were designed to fail in flexure, with safe shear capacity. It was considered necessary to test the beams with a realistic span-to-depth ratio that is appropriate and typically used in the design of bridge girders. Five beams had rectangular section of 150mm wide and 250mm deep. The rest of the beams were T-section with the same depth and web dimensions as the rectangular ones. Their flanges were 50 mm deep, while the widths were 350mm for seven of them and 550mm for the last one. All the prestressing cables of the tested beams were jacked to 75% of their ultimate stress. All the beams were reinforced with closed stirrups of 10mm diameter with spacing 100mm for the first 1400mm and 200mm for the rest of the beam. All the beams were reinforced using two conventional longitudinal reinforcement of 10mm diameter as a top reinforcement with 25mm cover. The end zone was reinforced by extra stirrups for the first 300mm with stirrup spacing of 50mm. Figure 1 shows the specimen’s typical reinforcement details. The designation for each beam has the first letter as R, T which indicates the shape of beam section as a rectangular or a T-section. The beam with wide flange of 550mm is followed by the symbol (*). The first number represents the targeted concrete compressive strength, which ranges from 45 MPa to 100 MPa. The second number has the value of 1,2 or 3 which represents different prestressing steel ratios that range from 0.31% to 0.61%. The third number also has the value of 1,2 or 3 but indicates the different conventional reinforcement ratios that range from 0.17% to 0.95%. Table 1 gives the specimen details.
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Figure 1. Specimen’s typical reinforcement details Table 1. Specimen details Specimen Code
Cross Section Type
prestressing steel
Prestressing steel ratio (%)
Conventional steel
Conventional steel ratio (%)
R-85-1-2 T-85-2-2 R-45-1-2 R-100-1-2 T-45-2-2 T-100-2-2 R-85-2-2 R-85-3-2 T-85-1-2 T-85-3-2 T-85-2-1 T-85-2-3 T-85-1-2*
R T R R T T R R T T T T T
1 (0.5”) 1 (0.6”) 1 (0.5”) 1 (0.5”) 1 (0.6”) 1 (0.6”) 1 (0.6”) 2 (0.5”) 1 (0.5”) 2 (0.5”) 1 (0.6”) 1 (0.6”) 1 (0.5”)
0.31 0.43 0.31 0.31 0.43 0.43 0.43 0.61 0.31 0.61 0.43 0.43 0.31
2T10 2T10 2T10 2T10 2T10 2T10 2T10 2T10 2T10 2T10 2T6 4T10 2T10
0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.17 0.95 0.48
Concrete compressive strength (MPa) 84.5 84.5 46.5 101 46.5 101 84.5 84.5 84.5 84.5 84.5 84.5 84.5
Study Parameter
Control for rectangular sections Control for T-sections Concrete compressive strength Concrete compressive strength Concrete compressive strength Concrete compressive strength Prestressing reinforcement ratio Prestressing reinforcement ratio Prestressing reinforcement ratio Prestressing reinforcement ratio conventional reinforcement ratio conventional reinforcement ratio Flange width (b=550)
Material properties Three different concrete mixes were used achieving 46.5, 84.5 and 101 MPa as an average 28-days cube compressive strength. Uncoated 7 wire strands of 1860 MPa tensile strength and 1670 MPa yield strength were used. All conventional reinforcement used as described in Table 1 was either 6 or 10 mm diameter, the nominal yield tensile strength of each were 240 MPa and 400 MPa respectively. Instrumentation The instrumentation used at the test setup is shown in Figure 2.a and 2.b. The concrete strain at the top surface and at the bottom reinforcements at the mid span and at the location of the applied load using electrical strain gauges. The readings were recorded via a data acquisition system at each loading step using a computer program. A thru-hole load cell was positioned between the anchor plate and the beam’s end plate to accurately measure the loss of prestressing force. The cracks were also monitored during the test at the conventional reinforcement level, through different load levels up to failure using a crack microscope of 0.025mm accuracy. Test setup and loading procedure The beams were tested using a quasi-static four point loading scheme till failure. The loads were applied 1400mm apart from the supports. Two cycles were applied till reaching 80% of the cracking load then released to ensure the behaviour linearity before cracking. Another two cycles were applied till reaching the first visible crack(s) then ###-3
released to study the behaviour of the beams after stiffness reduction due to cracking. Finally, the beams were loaded to failure.
Figure 2.a Schematic instrumentation of the test setup
Figure 2.b Test setup
2. EXPERIMENTAL RESULTS General observations The cracking behaviour of the tested partially prestressed beams was examined within the constant moment zone. Generally, it was observed that all cracks initiated at the constant moment zone, perpendicular to the center line of the beam. It was also observed that the stirrups acted as crack initiators for most of the flexural cracks which agrees with the findings of Dawood and Marzouk (2012). Figure 3 illustrates the typical crack width increase versus the ratio of the applied load to the ultimate load, where the linear and the parabolic relationship could be observed within and beyond the service limit (load causing 0.2mm crack width, where it is considered the border at which the experiences indicates that the cracks can be visible as mentioned by Abdelrahman (1995)) respectively as stated by El-Hashimy (2014). This concurred with Suri et al. (1986) findings for the high strength concrete.
Figure 3. Typical crack width propagation Crack pattern The crack pattern is defined by the crack spacing, height and width. Most of the recent researchers and design codes pay attention to the crack width as a crack controlling criteria. Figure 4 depicts the crack propagation for the studied beams at a maximum crack width of 0.2mm within the constant moment zone. From this figure, it can be observed that the crack spacing is controlled by the stirrups as it acts as crack initiators, as long as, the distance between stirrups does not exceed the required distance to develop a new crack between them. Crack height was found to be directly proportional to the concrete compressive strength and the compression flange width However it was inversely proportional to the prestressing and conventional reinforcement ratio, which is attributed to the lower location of the neutral axis leaving a larger compression block free of cracks as mentioned by Salem (2014). Figure 5 shows the propagation of the maximum crack width with respect to the ratio of applied to ultimate load. From this graph, it could be inferred that the concrete compressive strength and the prestressing steel ratio had a negligible effect on the maximum crack width if compared with the ratio of the applied to the ultimate load till 0.2mm crack width, which is considered the maximum permissible crack width given by different design codes. After that, it can be seen that the concrete compressive strength is directly proportional to the maximum crack width. Meanwhile, ###-4
maximum crack width had an inversely proportional relationship with the prestressing steel ratio and conventional reinforcement ratio. It is also noticed that the maximum crack width is directly proportional to the compressive flange width even when comparing with the ratio of the applied load to the ultimate one.
Figure 4. Crack propagation at maximum crack width of 0.2mm
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(a) Influence of concrete compressive strength
(b) Influence of prestressing steel ratio
(c) Influence of conventional reinforcement ratio
(d) Influence of compressive flange width
Figure 5. Maximum crack width propagation 3. ANALYTICAL PROGRAM The following section contains a statistical analysis for the main factors controlling the crack width propagation. This analysis used to validate the previously proposed equations for the crack width prediction using high strength concrete. Description and results of the application for several crack width prediction equations by different researchers and design codes have been also mentioned. The maximum crack width has been predicted till maximum crack width of 0.45mm. The predicted results with ±40% variation, along with the measured results have been illustrated at different graphs. This variation was proposed by the ACI Committee 224 (2001) based on the findings of (Leonhardt 1977). Major variables controlling crack width Many variables influencing the crack width propagation have been mentioned earlier. However, the steel stress after decompression is considered the most important parameter according to Suri and Dilger (1986). A correlation analysis was performed to validate the linear relationship between the maximum crack width and the conventional steel stress suggested by Suri and Dilger (1986) for partially prestressed high strength concrete beams. The correlation coefficient was used as a quantitative measurement for the linearity of the relationship between the two variables. Figure 6 validates the linear relationship suggested by Suri and Dilger (1986) for high strength concrete during the service loads under the influence of changing the prestressing steel ratio, conventional steel ratio and the compression flange width. Most of the crack width prediction equation is either function of the stress at the prestressing or the conventional steel. During this investigation, the stress is calculated using the cracked transformed analysis suggested by Mast (1998).
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Figure 6. Relation between conventional steel stress and maximum crack width Canadian Precast/Prestressed Concrete Institute “CPCI Design Manual” (2007), Suri and Dilger (1986) The CPCI (2007) recommended the use of Equation 1, which was purposed by Suri and Dilger (1986) with changing the value of the constant k1 to account for the combination of the deformed bars and strands and for strands only. The maximum crack width resulted from the experimental program have been plotted against the results using the CPCI recommended equation at Figure 7. Table 2 shows the statistical results for the error between the measured and the predicted crack widths using the CPCI Design Manual (2007). [1] Wmax
k1fsdc
Where Wmax k1 dc Ar Ast
Ar Ast
= maximum crack width. = 3x10-6 for a combination of deformed bars and strands and for strands only. = concrete cover to center of reinforcement. = concrete area in tension below the neutral axis. = prestressed steel area and the equivalent non prestressed steel area.
Figure 7. Crack width prediction according to the CPCI design manual (2007) Euro Code 2 “EC2” (2002) Euro Code 2 (2002) suggested the use of Equation 2 for the crack width prediction. This approach is derived as a result of dividing the sum of all crack widths at any level (average strain of the reinforcement steel per unit length) and the number of cracks per unit length given by an empirical equation. The maximum crack width resulted from the experimental program have been plotted against the results using the Euro Code equation at Figure 8. Table 2 shows the statistical results for the error between the measured and the predicted crack widths using EC2. [2] wk = sr, max (sm - cm) Where Sr,max εsm εcm
= maximum crack spacing. = mean strain at the reinforcement under the relevant combination of loads. = mean strain in concrete between cracks.
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Figure 8. Crack width prediction according to the EC 2 (2002) Gregely and Lutz (1968) The equation proposed by Gregely and Lutz (1968) for the maximum crack width prediction has been suggested by the CPCI Design manual (2007). Figure 9 presents a comparison between the measured and predicted maximum crack widths according to the equation proposed by Gregely and Lutz (1968) and given at Equation 3. Table 2 shows the statistical results for the error between the measured and the predicted crack widths using the GregelyLutz equation.
[3] w R f ps 3 d c A Where fps dc A β
= tensile stress in prestressed reinforcing steel. = concrete cover to center of closest bar layer. = concrete tensile area per bar. = ratio of distances from tension face and steel centroid to neutral axis.
Figure 9. Crack width prediction according to the Gregely and Lutz (1968) Japan Society of Civil Engineers “JSCE” (2010) Equation 4 presents the proposed equation by the JSCE (2010) for the maximum crack width prediction. It has been applied at the studied beams and a comparison of the measured crack widths is presented at Figure 10. Table 2 shows the statistical results for the error between the measured and the predicted crack widths using JSCE (2010). [4]. w
1.1k 1 k 2 k 3 [4c 0.7(C s )].[
Where k1 k2 k3 c Cs
pe Ep
csd ]
= constant to take into account the effect of surface geometry of reinforcement on crack width. = constant to take into account the effect of concrete quality on crack width. = constant to take into account the effect of concrete quality on reinforcement arrangement. = concrete cover. = center-to-center distance of tensile reinforcements. ###-8
pe
= equivalent prestressing and conventional steel area. = increment of stress of prestressing steel from the state in which concrete stress at the portion of reinforcement is zero. csd = compressive strain for evaluation of increment of crack width due to shrinkage and creep of concrete. Ep = prestressing steel young’s modulus.
Figure 10. Crack width prediction according to the JSCE (2010)
Table 2. Statistical analysis results for the errors of crack width prediction using various predicting equations
CPCI manual (2007)
Number of data 51
Mean error % -0.1
Standard deviation 64.5
Maximum error 82
Minimum error -269
Euro Code 2 (2002)
51
37.6
39.7
89
131
Gregely and Lutz (1968)
51
2.2
64.6
50
-300
JSCE (2010)
51
-1.2
70.0
85
-265
4. CONCLUSIONS From the observations of the experimental work reported and the results of the statistical analysis performed at the analytical program for partially prestressed concrete beams, the following conclusions could be drawn: The crack height was found to be directly proportional to the concrete compressive strength and the compression flange width However it was inversely proportional to the prestressing and conventional reinforcement ratio, which is encountered to the location of the neutral axis. The concrete compressive strength and the prestressing steel ratio had a negligible effect on the maximum crack width if compared with the ratio of the applied to the ultimate load till 0.2 mm crack width. However, it is directly proportional to the concrete compressive strength and the prestressing steel ratio. Maximum crack width had an inversely proportional relationship with the conventional reinforcement ratio and directly proportional with the compressive flange width even when comparing with the ratio of the applied load to the ultimate one. Results showed that the parabolic shape of the crack width increase is valid for partially prestressed high strength concrete beams. The equation given by CPCI (2007) for crack width computation gave the best mean error but with a high standard deviation when compared with the EC2.
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5. REFERENCES Karayannis, C.G., Chalioris C.E. 2012. Design of partially prestressed concrete beams based on the cracking control provisions. Engineering Structures 48(2013): 402–416. A.A. Abdelrahman 1995. Serviceability of Concrete Beams Prestressed by Fiber Reinforced Plastic Tendons. Ph.D Thesis, University of Manitoba, Manitoba, Canada. Dawood N. and Marzouk H. 2012.Cracking and Tension Stiffening of High Strength Concrete Panels. ACI Structural Journal, 109 (1): 21-30. American Concrete Institute (ACI) 2011.Building Code Requirements For Reinforced Concrete (ACI 318M-11), Farmington Hills, Michigan, USA: 01-503. Suri K.M. and Dilger W.H. 1986. Crack width of Partially Prestressed Concrete Members. ACI Structural Journal, 83 (5): 784-797. Mast R.F. 1998. Analysis of Cracked Prestressed Concrete Sections : A Practical Approach. PCI Journal, 43 (4): 80-91. Canadian Precast / Prestressed Concrete Institute 2007. CPCI Design Manual 4. Ottawa, Ontario. Comité Européen de Normalisation (CEN) 2002. Eurocode 2: Design of concrete structures - Part 1: General rules and rules for buildings. Vols. prEN 1992-1. Japan Society of Civil Engineers (JSCE) 2010. Standard Specification For Concrete Structures-2007 "Design". Subcommittee on English Version of Standard Specification for Concrete Structures-2007, Tokyo, Japan. ACI Committee 224 2001.Control of Cracking in Concrete Structures (224R-01). American Concrete Institute, Farmington Hills, Michigan, MI, USA: 01-46 El-Hashimy T.H. 2014. Serviceability of Partially Prestressed High Strength Concrete T-section beams. Submitted MSc thesis for approval, Ain Shams University, Cairo, Egypt. Salem S.H. 2014. Behavior of Rectangular Partially Prestressed High Strength Concrete Beams . Submitted MSc thesis for approval, Ain Shams University, Cairo, Egypt.
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